1. Case Study - Group 2 FCC-ee Top-Up Injection
Dmitriy Berkaev (BINP SB RAS)
Johannes Bernhard (CERN)
Szymon Myalski (EBG MedAustron GmbH)
Shuang Ruan (Chinese Academy of Sciences)
Michaela Schaumann (CERN)
Christoph Wiesner (CERN)

2. Luminosity and Injection Time
Lumi life time t = 1 hour
Minimum Beam Length: 75 us (for 2.5 ns bunch spacing)
Collider Parameters
Beam Energy (GeV)
175
45.6
Number of bunches 81
30 180
Rev. time
334 us
RF frequency
400 MHz
Harmonic number
Design goal:
L/L0 = 99 %
Conclusion: Possibility of flexible filling/injection pattern
Conclusion: High top-up injection rate required 1

3. Injection Scheme
Conventional injection scheme based on static septum and dynamic bump
Challenges:
Inject into small dynamic aperture
Kicker stability
Drawing: M. Aiba, CAS’17
15s
150 m
500 m
200 m
500 m
150 m 2

4. Injection Scheme
Conventional injection scheme based on static septum and dynamic bump
Required horizontal deflection:
Challenges:
Inject into small dynamic aperture
Kicker stability
< 15s
Stored and injection beta funct.: bcirc, binj
dsept: Septum thickness
n , m: Clearances in units of beam size
Drawing: M. Aiba, CAS’17 D
150 m
500 m
200 m
500 m
150 m 2

5. Injection Scheme
Conventional injection scheme based on static septum and dynamic bump
Required horizontal deflection:
Challenges:
Inject into small dynamic aperture
Kicker stability
< 15s
Stored and injection beta funct.: bcirc, binj
dsept: Septum thickness
n , m: Clearances in units of beam size
Drawing: M. Aiba, CAS’17
15s
150 m
500 m
200 m
500 m
150 m
Use dispersion suppressor. Assuming zero dispersion in injection region.
No optic elements. (Defocusing quad. could be used to amplify kick). D 2

6. Optimizing Parameters
Matched injection preferable but not mandatory for lepton beam
Approach: Reduce binj and injection clearance n to be able to increase clearance m for stored beam (while staying inside dynamic aperture)
Example:
n = 3
m = 5
bcirc = 2 km
binj = 100 m
dsept = 5 mm
Kicker length = 1 m
Required kicker field: B = 18 mT
for kick angle a = 30 urad
Dmin: required horiz. deflection
Stored and injection beta funct.: bcirc, binj
dsept: Septum thickness
n , m: Clearances in units of beam size 3

7. Kicker Error
Conclusion: Luminosity loss only relevant for very high repetition rate of top up injections.
However: Beam could become unstable (beam-beam effect…).
Kick angle θk = 50 µrad
βy* = 1 mm
βx* = 1 m
Worst case: 90o phase advance between kicker and IP
Luminosity change due to displacement during injection: ΔL/L = 1 - exp{-δ12/(2βε)}
Error
Δθk/θk
Displacement
vertical injection
horizontal injection
ΔL/L vertical injection
ΔL/L horizontal injection 1%
0.7 µm (0.6 σ)
22 µm (0.6 σ)
17.5%
0.1%
0.07 µm (0.06 σ)
2.2 µm (0.06 σ)
0.2%
Possible injection duty cycles: Low rep. rate  10 ms/18 s = 5.6e-4
High rep. rate  10 ms/0.1 s = 0.1 4

8. Hardware: Kicker & Septum
Lambertson-Septum with 5 mm septum blade (vertical injection, horizontal bump).
Bump Kicker: Vertical gap size does not seem critical.
Fast Kicker:
GTO Stack: long flat-top length (~100us), low flat-top stability
Marx Generator: long flat-top length (>100us), high flat-top stability (< 1%)  Injection of long pulse trains possible
Inductive Adder: short flat-top length (~ few us), very high flat-top stability (~0.02%, see CLIC-DR kicker), short rise and fall time (<100 ns)  Injection of short pulses with high repetition
To be confirmed. 5

9. Failure Scenarios
Assumption: Injected beam energy should be limited to 5 MJ
 5 (initial) injections required
not critical for top-up injected beam
Collider Parameters
Beam Energy (GeV)
175
45.6
Number of bunches 81
30180
Bunch Intensity
1.7e11
1e11
Stored beam energy (MJ)
0.4 22
Max # bunches / injection
1048
6844
# of initial injection required 1 5
Injected beam energy / top-up cycle (MJ)
4e-3
0.22
Protection elements
Conclusion: Missing injection kicker seems less critical than erratic misfiring on stored beam ( retriggering?). 6

10. Thank you for your attention!

11. Gaining Dynamic Aperture?